There are many applications in which the small size of the antennas is a desirable feature due to cosmetic, security, aerodynamic and other reasons. There are also applications in which surface conformability of the antennas or a possibility to mount an antenna on a platform, which is not flat or planar, is a desirable feature.
For example, in mobile devices (e.g., cellular phones, PDAs, laptops, etc), reducing antenna's size is required since the amount of space available for mounting an antenna is limited. For antennas mounted on airplanes, the protrusion of the antenna beyond the surface of the plane should be minimized in order to reduce the effect of the antenna on its aerodynamic properties.
Fractal antennas are known in the art as solutions to significantly reduce the antenna size, e.g., from two to four times, without degenerating the performance. Moreover, applying fractal concept to antennas can be used to achieve multiple frequency bands and increase bandwidth of each single band due to the self-similarity of the geometry. Polarization and phasing of fractal antennas also are possible.
The self-similarity of the antenna's geometry can be achieved by shaping in a fractal fashion, either through bending or shaping a surface and/or a volume, or introducing slots and/or holes. Typical fractal antennas are based on fractal shapes such as the Sierpinski gasket, Sierpinski carpet, Minkovski patches, Mandelbrot tree, Koch curve, Koch island, etc (see, for example, U.S. Pat. Nos. 6,127,977 and 6,452,553 to N. Cohen).
Referring to FIGS. 1A to 1D, several examples of typical fractal antennas are illustrated.
In particular, the Triadic Koch curve has been used to construct a monopole and a dipole (see FIGS. 1A and 1B) in order to reduce antenna size. For example, the length of the Koch dipole antenna is reduced by a factor of 1.9, when compared to the arm length of the regular half-wave dipole operating at the same frequency. The radiation pattern of a Koch dipole is slightly different from that of a regular dipole because its fractal dimension is greater than 1.
An example of a fractal tree structure explored as antenna element is shown in FIG. 1C. It was found that the fractal tree usually can achieve multiple wideband performance and reduce antenna size.
FIG. 1D shows an example of a Sierpinski monopole based on the Sierpinski gasket fractal shape. The original Sierpinski gasket is constructed by subtracting a central inverted triangle from a main triangle shape. After the subtraction, three equal triangles remain on the structure, each one being half of the size of the original one. Such subtraction procedure is iterated on the remaining triangles. In this particular case, the gasket has been constructed through five iterations, so five-scaled version of the Sierpinski gasket can be found on the antenna (circled regions in FIG. 1), the smallest one being a single triangle.
The behavior of various monopole antennas based on the Sierpinski gasket fractal shape is described in U.S. Pat. No. 6,525,691 to Varadan et al., in a paper titled “On the Behavior of the Sierpinski Multiband Fractal Antenna,” by C. Puente-Baliarda, et al., IEEE Transact. Of Antennas Propagation, 1998, V. 46, No. 4, PP. 517–524; and in a paper titled “Novel Combined Multiband Antenna Elements Inspired on Fractal Geometries,” by J. Soler, et al., 27th ESA Antenna Workshop on Innovative Periodic Antennas: Electromagnetic Bandgap, Left-handed Materials, Fractals and Frequency Selective Surfaces, 9–11 Mar. 2004 Santiago de Compestele, Spain, PP.245–251. It is illustrated in these publications that the geometrical self-similarity properties of the fractal structure are translated into its electromagnetic behavior. It was shown that the antenna is matched approximately at frequencies
            f      n        ≈          0.26      ⁢              c        h            ⁢              δ        n              ,where c is the speed of light in vacuum, h is the height of the largest gasket, δ=2, and n a natural number. In particular, the lowest frequency of operation in such antennas is determined by the height of the largest gasket.
Various fractal loop antennas are also known in the art. For example, U.S. Pat. No. 6,300,914 describes a wideband antenna that operates at multiple frequency bands. The antenna is formed from a plurality of fractal elements either cascade connected, series connected or parallel connected. Each of the fractal elements are folded in a same plane of the fractal element to form a sawtooth pattern.